Answer: A) 67[tex]\frac{11}{117}[/tex] (or) 67.09
B) No. of people neither children nor women
= 468-(314+75)
= 79
= [tex]\frac{79}{468}[/tex]*100
= 16[tex]\frac{103}{117}[/tex] (or) 16.88
I hope it helps. Have a great day :)
Answer:
a) = 67.10 % or 67.09%
b) = 84.10% or 83.97%
Step-by-step explanation:
a = (314/468)*100 = 67.094017094 %
b = (393/468)*100 = 83.9743589744 % (edited 393)
To find b we have to can use simple subtraction to find Men = m = ?
If Women = w = 314 and Children = c = 75
Eliminate the (w = 314) with (c=75) from total to find (m=?)
w+c+m= 468
c+m = 468-w = 468-314 = 154
m = 154-c = 154-75 = 79
m = 79
b) Total sum that were not children = w+m = 314 + 79 = 393
or = 468-314 = 154
then 154 - 79 = 75
with = 468-75 = 393
then find percentage;
(393/468) * 100 = 83.9743589744
Circles
1. RS and ST are tangent lines. Find the value of x.
R
9x - 30
c.
S
3x
T
Answer:
x = 15
Step-by-step explanation:
9x-30 = 3x (tangent lines are congruent)
- move the variables to one side
9x-3x=30
6x=30
x=5
--------------
9(5)-30=3(15)
45-30=15
15=15
Done!
Find all real zeros of the function.
g(x) = 2x (x - 5)2(x – 9)?
If there is more than one answer, separate them with commas.
zero(s):
Answer:
0, 5, 9
Step-by-step explanation:
g(x) = 2x (x - 5)^2(x – 9) = 0
x = 0 or x - 5 = 0 or x - 9 = 0
x = 0 or x = 5 or x = 9
help me plz i wnt help plz i want help
Answer:
C)28in
Step-by-step explanation:
To get the area of this face, we will divide it into 3 sections.
Area of the 1st section:
Given:
l=4in
w=2in
Formula:
a=l*w
Solution:
a=l*w
a=8in^2
Area of the 2nd section:
Given:
l=2in
w=2in
Formula:
a=l*w
Solution:
a=l*w
a=2in*2in
a=4in^2
Area of the 3rd section:
l=8in
w=2in
Formula:
a=l*w
Solution:
a=l*w
a=8in*2in
a=16in^2
a1+a2+a3=Area of the face
8in^2+4in^2+16in^2=28in^2
Hope this helps ;) ❤❤❤
Town B is 250 km from town A on a bearing of 080°.
Town C is 250 km from town B on a bearing of 220°.
What is the bearing from town A to town C?
Answer:
Step-by-step explanation:
P. The inventory of a store 2 years ago was worth $45,000. This year it is
worth $49,500. What is the percent increase? Show your work
Answer:10% increase
Step-by-step explanation:
49500-45000=4500
4500/45000=0.1
0.1x100=10
10% increase
Answer:
10%
Step-by-step explanation:
follow the rules of calculating percentages.
fractions, decimals, etc.
pls mark brainliest
if f(x) -3 and g(x) = 3x2+x-6, find (f+9)(x).
A. 4x2 - 9
B. 3x2 + x - 3
C. 3x2 + 2X-9
D. 3x2 - 4x = 3
Answer:
3x^2 +x -3
Step-by-step explanation:
f(x)= 3 and g(x) = 3x^2+x-6
f+g (x) = 3+ 3x^2+x-6
Combine like terms
= 3x^2 +x -3
Kate wants to paddle
her canoe across the lake. To determine how far she must paddle, she paced out a triangle,counting the number of strides, as shown.
If Kate's strides average 3.5 ft, what is the
length of the longest side of the triangle?
What distance must Kate paddle across
the lake?
Answer:
1. Length of longest side of the triangle = 1,050 ft
2. Length = 437.5 ft
Step-by-step explanation:
Given:
Kate's strides average = 3.5 ft
Find:
1.longest side of the triangle
2.Distance must Kate paddle across the lake
Computation:
1.longest side of the triangle
longest side of the triangle = AE
So,
longest side of the triangle = 150 + 150
longest side of the triangle = 300
Length of longest side of the triangle = 300 × 3.5 ft
1. Length of longest side of the triangle = 1,050 ft
2.Distance must Kate paddle across the lake.
We know that,
ΔABD ~ ΔACE
So,
AB / AC = BD / CE
80 / 160 = BD / 250
BD = 125 Strides
Length = 125 × 3.5 ft
2. Length = 437.5 ft
Simplify (−3c3w5)3. −9c6w8 −9c9w15 −27c6w8 −27c9w15
Answer:-9c3w5-36c6w8-36c9w15
Answer:
-27c⁹w¹⁵ the last choice
Step-by-step explanation:
Simplifying:
(−3c³w⁵)³= ⇒ each factor gets same power- 3³(c³)³(w⁵)³ = ⇒ power of power = product of powers- 27c⁹w¹⁵ ⇒ correct answer choice is the last oneWhich of the following is a graph of f(x) =square root of x +5
Answer:
Step-by-step explanation:
You didn't include any graphs, so I can't tell you which one it is. However, the graph of [tex]f(x)=\sqrt{x+5}[/tex] looks like this:
Hope this helps!
The graph of the function [tex]\rm f(x) = \sqrt{x+5}[/tex] is attached below and this can be determined by using the rules of transformation.
Given :
[tex]\rm f(x) = \sqrt{x+5}[/tex]
The following steps can be used in order to sketch the graph [tex]\rm f(x) = \sqrt{x+5}[/tex]:
Step 1 - The rules of transformation can be used in order to sketch the graph [tex]\rm f(x) = \sqrt{x+5}[/tex].
Step 2 - First draw the graph of [tex]\sqrt{x}[/tex] which is in the shape of a parabola.
Step 3 - Now, translate the graph in the left direction, So the function of the graph obtained is [tex]\rm f(x) = \sqrt{x+5}[/tex].
The graph of the function [tex]\rm f(x) = \sqrt{x+5}[/tex] is attached below.
For more information, refer to the link given below:
https://brainly.com/question/14375099
Find the area of the shape shown below.
Answer:
31.5
Step-by-step explanation:
We can add the areas together
We have a rectangle and a triangle
The area of the rectangle is
A = lw
= 7*3
= 21
The area of the triangle is
A = 1/2 bh
= 1/2 (7)*3
= 21/2
= 10.5
Add them together
A = 21 + 10.5
=31.5
Answer:
31 1/2
Step-by-step explanation:
You find the area for the triangle on top and the rectangle on the bottom. In order to find the area of the triangle, multiply 7 and 3. Then divide the product which is 21 by 2. So the area of the triangle is 21/2 which could also be written as 10 1/2. Next, you find the area of the rectangle which is 7x3. You get 21. Finally, you add the two areas to get 31 1/2. It could also be written as 63/2 or 31.5
Graph the solution of 7x+3<−4 or 2x−3≥9
Answer:
Step-by-step explanation:
To do this you would simplify both sides.
For the first one:
[tex]7x+3<-4[/tex]
[tex]7x<-7[/tex] (subtract 3 from both sides)
[tex]x<-1[/tex] (divide 7 from both sides)
and for the second one:
[tex]2x-3\geq 9[/tex]
[tex]2x\geq 12[/tex] (add 3 to both sides)
[tex]x\geq 6[/tex] (divide 2 from both sides)
When you graph these they will look like these pictures
Answer:
[tex]x<-1[/tex] and [tex]x\geq6[/tex]
Step-by-step explanation:
[tex]\bf 7x+3<-4[/tex]
You must subtract 3 from both sides.
[tex]7x+3-3<-4-3\\[/tex]
After subtracting, we got
[tex]7x<-7[/tex]
Let's make it into a fraction and divide
[tex]\frac{7x}{7}<\frac{-7}{7}[/tex]
Now we got the answer
[tex]x<-1[/tex]
[tex]\bf 2x-3\geq 9[/tex]
You must add 3 to both sides.
[tex]2x-3+3\geq 9+3[/tex]
After adding, we got
[tex]2x\geq 12[/tex]
Let's make it into a fraction and divide
[tex]\frac{2x}{2} \geq \frac{12}{2}[/tex]
Now we got the answer
[tex]x\geq 6[/tex]
Your answer is [tex]\bf x<-1[/tex] or [tex]\bf x\geq 6[/tex].
The members of a film crew are at least 75 miles from their camp and must carry equipment back to camp before a storm arrives. The storm is scheduled to begin in 24 hours. They plan to travel as far as possible by truck and then walk the rest of the way. The truck can travel at a rate of 10 miles per hour through the terrain, and the team can travel 2 miles per hour on foot. Which system represents the number of hours the crew can travel by truck, x, and on foot, y, to reach camp before the storm? x + y < 24 2x + 10y ≥ 75 x + y > 24 2x + 10y ≥ 75 x + y < 24 10x + 2y ≥ 75 x + y > 24 10x + 2y ≥ 75
Answer:
I DONT UNDERSTAND ANY OF THIS
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
On a map’s coordinate grid, Panthersville is located at (−3, 2), and Heel City is located at (4, 8). Falconton is the midpoint between Panthersville and Heel City. What is the approximate distance from Panthersville to Falconton? (Each unit on the grid represents 1 mile.) A. 3.25 miles B. 4.61 miles C. 5.00 miles D. 9.22 miles
Answer:
The approximate distance from Panthersville to Falconton is: B: 4.61 miles.
Step-by-step explanation:
Objective: Find the distance from Panthersville to Falconton. (Which is just half of the distance from Panthersville to Heel City because Falconton is the midpoint between both cities.)
First we need to find the distances from Panthersville to Heel City, which we are given the coordinates. ( Panthersville (-3,2) & Heel City (4, 8) )
-To find the distance between the two cities we use the distance formula:
d= √(x2 - x1) ^2 + (y2 - y1)^2 , so we set (-3,2) as x1 and y1 while (4,8) x2 and y2 and we just plug it in.
Once we plug it in we get:
d= √(4 - -3)^2 + (8 - 2) ^2
Then we solve the numbers in the parenthesis (4 - -3) = 7 and (8 - 2) = 6 so now we have:
d= √(7)^2 + (6) ^2
Next we solve for the exponents (7)^2 = (7 x 7 = 49) and (6)^2 = ( 6 x 6= 36) now it look like this:
d= √49 + 36
After that we just add both numbers together (49 + 36) = 85
d= √85
Now all we have to do is square root 85 which is just 9.219544457, just round it to the nearest hundredth and you will get 9.22.
So the distance from Panthersville to Heel City is about 9.22 miles.
Now we found the full distance we now need to find the distance from Panthersville to Falconton which is just half of that distance due to Falconton being the midpoint.
All we have to do is divide 9.22 by 2 and we get 4.61.
The distance from Panthersville to Falconton is 4.61 miles.
Which relation is a function? {(–4, –6), (–3, –2), (1, –2), (1, 0)} {(–2, –12), (–2, 0), (–2, 4), (–2, 11)} {(0,1), (0, 2), (1, 2), (1, 3)} {(8, 1), (4, 1), (0,1), (–15, 1)}
Answer:
[tex]\{(8, 1), (4, 1), (0,1), (-15, 1)\}[/tex]
Step-by-step explanation:
Given
[tex]\{(-4, -6), (-3, -2), (1, -2), (1, 0)\}[/tex]
[tex]\{(-2, -12), (-2, 0), (-2, 4), (-2, 11)\}[/tex]
[tex]\{(0,1), (0, 2), (1, 2), (1, 3)\}[/tex]
[tex]\{(8, 1), (4, 1), (0,1), (-15, 1)\}[/tex]
Required
Determine which is a function
A relation is divided into 2; (x,y)
Where x represents the range and y stands for the domain
For a relation to be a function, the x column must be unique; in other words, there must be only one occurrence of x
Testing each of the given options
A. [tex]\{(-4, -6), (-3, -2), (1, -2), (1, 0)\}[/tex]
Start by splitting the relation into x and y columns
[tex](x,y)[/tex]
[tex](-4, -6)[/tex]
[tex](-3, -2)[/tex]
[tex](1, -2)[/tex]
[tex](1, 0)[/tex]
Notice that the third and fourth relation has the same x value of 1;
Hence, this is not a function
B. [tex]\{(-2, -12), (-2, 0), (-2, 4), (-2, 11)\}[/tex]
Start by splitting the relation into x and y columns
[tex](x,y)[/tex]
[tex](-2, -12)[/tex]
[tex](-2, 0)[/tex]
[tex](-2, 4)[/tex]
[tex](-2, 11)[/tex]
Notice that all relations has the same x value of -2;
Hence, this is also not a function
C. [tex]\{(0,1), (0, 2), (1, 2), (1, 3)\}[/tex]
Start by splitting the relation into x and y columns
[tex](x,y)[/tex]
[tex](0, 1)[/tex]
[tex](0, 2)[/tex]
[tex](1, 2)[/tex]
[tex](1, 3)[/tex]
Notice that the first and second relation has the same x value of 0 and the third and fourth relation has the same x value of 1;
Hence, this is also not a function
D. [tex]\{(8, 1), (4, 1), (0,1), (-15, 1)\}[/tex]
Start by splitting the relation into x and y columns
[tex](x,y)[/tex]
[tex](8, 1)[/tex]
[tex](4, 1)[/tex]
[tex](0, 1)[/tex]
[tex](-15, 1)[/tex]
Notice that relation has the unique x values of 8, 4, 0 and -15
Hence, this relation is a function
Please help me with this!!!
Answer:
(f•g)(2)=3 and (g•f)(6)=7
Step-by-step explanation:
look at the tables
where x is equal to both 2 and 7 is where you will find your answer
Hope this helps you!
simplified?
[tex]5 \sqrt{ - 8r} [/tex]
Im just confused on how the negative 8 will play out, and same with the non exponential variable.
Answer:
[tex]10i\sqrt{2r}[/tex].
Step-by-step explanation:
[tex]5\sqrt{-8r}[/tex]
= [tex]5\sqrt{-1 * 2 * 2 * 2 * r}[/tex]
= [tex]5i\sqrt{2^2 * 2 * r}[/tex] (i = the square root of -1)
= [tex]5i * 2\sqrt{2 r}[/tex]
= [tex]10i\sqrt{2r}[/tex]
Hope this helps!
5.4(m-2)= -2(3m+3) please help asap
Answer:
m = 0.421
Step-by-step explanation:
5.4(m-2)= -2(3m+3) (expand parentheses by distributive property)
m(5.4) -2(5.4) = 3m(-2) + 3(-2)
5.4m - 10.8 = -6m - 6 (add 6m to both sides)
5.4m - 10.8 + 6m = - 6
11.4m - 10.8 = - 6 (add 10.8 to both sides)
11.4m = -6 + 10.8
11.4m = 4.8 (divide both sides by 11.4)
m = 4.8 / 11.4
m = 0.421
Answer:
m = 8/19
Step-by-step explanation :
5.4 (m-2) = -2 (3m +3)
54/10 (m-2) = (3m +3) as n = 1
2.3^3 / 2.5 (m-2) = (3m + 3)
4.868 (m-2) = (3m +3)
4.868 + 3 = (3m^2 * m-2)
8 / 9.5 * 2
m = 8 / 19
Rearrange the tiles so that it shows the proper steps of solving this quadratic equation using square property
Answer:
see explanation
Step-by-step explanation:
Given
(x + 2)² = 25 ( take the square root of both sides )
x + 2 = ± [tex]\sqrt{25}[/tex] ← Step 1
x + 2 = ± 5 ← Step 2 ( subtract 2 from both sides )
x = - 2 ± 5 ← Step 3
help plz help me .me no good
Answer:
50,000,000
Step-by-step explanation:
5 * 10 ^7
The 7 in the exponent means move the decimal 7 places to the right
5. We need to add 7 zeros
50000000
50,000,000
Which statement best compares the two functions?
The minimum of function A occurs 1 unit higher than the minimum of function B.
The minimum of function A occurs 3 units higher than the minimum of function B.
The minimum of function A occurs 5 units lower than the minimum of function B.
The minimum of function A occurs 7 units lower than the minimum of function B.
Answer:The minimum of function A occurs 1 unit higher than the minimum of function B.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Trust
pls help...1.The given right rectangular prism is composed of small cubes. Find the following is the volume of the prism and the volume of one of the small cubes.
Answer:
1. 1.3778 2. 0.0089
Step-by-step explanation:
to find the volume of the whole rectangle prism you would have to do the volume formula since it is a 3d shape. VOLUME FORMULA, LxWxH.
so 1x0.83x1.66= 1.3778
you can always convert the fraction into decimal to help you calculate the problem.
i don't know if this is correct but i give it a try, so if the whole volume of the triangle is 1.3378 than you can divide that by the the number of small cubes it has inside.
it is 5 by 10 so there are 150 cubes in total.
1.3378 divided by 150=0.0089
im confident about the 1st but not so much with the second
The volume of the rectangular prism is: 1.39 ft³
The volume of one of the small cubes is: 0.0046 ft³
What is the Volume of a Rectangular Prism?Volume of rectangular prism = length × width × height
Given the following:
Length = 1 ft
Width = 5/6 ft
Height = 1⅔ ft
Volume of the rectangular prism = 1 × 5/6 × 1⅔ = 1 × 5/6 × 5/3
Volume of the rectangular prism = 25/18 = 1 7/18 ft = 1.39 ft³
Length of the edge of 1 cube = 1/6 ft
Volume of the 1 cube = (1/6)³ = 1/216 = 0.0046 ft³
Learn more about volume of rectangular prism on:
https://brainly.com/question/12917973
Find the measure of c.
Answer:
140°
Step-by-step explanation:
The circle has a central angle of 80. This means that the arc it intercepts is also 80°. Therefore, the rest of the circle not intercepted by the arc is 360-80=280°
Remember that inscribed angles have one-half of the arc-length it intercepts. We can see that Angle C intercepts the entire circle except for the arc intercepted by Angle O. Therefore, the arc intercepted by Angle C is 280°. This means that Angle C is the half of 280, or 140°.
Write the equation for the following table:
0 2
1 7
2 13
3 20
Answer:
Step-by-step explanation:
for each positive integer m, so that la - r2m-ll and la - r2m I are both less than
1 1
Ir2m - r2m-ll .:::: 42(m-l) Ir2 - rll = 24m - 3 ·
It follows that limn--->oo rn = limn--->oo rn-l = a. Taking limits in the recursion in
(d) leads to
1
a=I+--
l+a
which reduces to a 2 = 2. Since rn > 0 for each n, a > O.
write the percent as a fraction or mixed number in simpelst form 35% A) 3 1/2 B) 13/20 C) 6 1/2 D) 7/20
Answer:
7/20
Step-by-step explanation:It is the same thing as .35. So just turn it into fraction and simplify.
Answer:
D) 7/20
Step-by-step explanation:
Divide 35 by 100:
35 / 100 = .35
Convert into a fraction and simplify:
[tex].35=\frac{35}{100}=\frac{35/5}{100/5}=\boxed{\frac{7}{20}}[/tex]
Option D should be the correct answer.
Name five fractions between 6/7 and 9/10
Answer:
43/50, 22/25, 111/125, 1111/1250, and 179/200.
Step-by-step explanation:
6/7 = 0.8571428571
9/10 = 0.9
The fractions can be anywhere within that range.
The first fraction I would name would be a fraction that equals 0.86. 0.86 = 86/100 = 43 / 50.
The second fraction can be a fraction that equals 0.88. 0.88 = 88 / 100 = 44 / 50 = 22 / 25.
The third fraction will equal 0.888. 0.888 = 888 / 1000 = 444 / 500 = 222 / 250 = 111 / 125.
The fourth fraction will equal 0.8888. 0.8888 = 8888 / 10000 = 4444 / 5000 = 2222 / 2500 = 1111 / 1250.
The fifth fraction can equal 0.895. 0.895 = 895 / 1000 = 179 / 200.
Hope this helps!
Answer:
43/50, 22/25, 111/125, 1111/1250, and 179/200.
Step-by-step explanation:
6/7 = 0.8571428571
9/10 = 0.9
The fractions can be anywhere within that range.
The first fraction I would name would be a fraction that equals 0.86. 0.86 = 86/100 = 43 / 50.
The second fraction can be a fraction that equals 0.88. 0.88 = 88 / 100 = 44 / 50 = 22 / 25.
The third fraction will equal 0.888. 0.888 = 888 / 1000 = 444 / 500 = 222 / 250 = 111 / 125.
The fourth fraction will equal 0.8888. 0.8888 = 8888 / 10000 = 4444 / 5000 = 2222 / 2500 = 1111 / 1250.
The fifth fraction can equal 0.895. 0.895 = 895 / 1000 = 179 / 200.
Write as an inequality. "Four more than half a number is at most sixteen"
1/2 + 4 ≤ 16
four more = +4
half a number = 1/2
at most means less or greater which is ≤
Answer:
0.5n + 4 ≤ 16
Step-by-step explanation:
add 4 to half of the unknown number (n). It is at most 16 (less than or equal to).
0.5n + 4 ≤ 16
the formula for a trapezoid is A= 1/2h(b1+b2) which equations are equivalent to the formula
Answer:
A=[tex]\frac{a+b}{2} (h)[/tex]
Step-by-step explanation:
Option first, option second, and option fourth are correct this expression is equivalent to the formula for a trapezoid.
What is a trapezoid?It is defined as the quadrilateral having four sides in which two sides are parallel to each other, it is a 2-dimensional geometry.
The options are:
h=2A/(b1+b2)b1=2A/h - b2b2= 2A/b1 - hb2= 2A/h - b1b1= 2A//b2 - hWe have a formula for finding the area of the trapezoid:
[tex]\rm A= \dfrac{1}{2}h(b_1+b_2)[/tex]
Make a subject h and solve for h:
[tex]\rm \dfrac{2A}{(b_1+b_2)}= h[/tex]
or
[tex]\rm h = \dfrac{2A}{(b_1+b_2)}[/tex]
[tex]\rm b_2 = \dfrac{2A}{h}- b_1[/tex]
[tex]\rm b_1 = \dfrac{2A}{h}- b_2[/tex]
Thus, option first, option second, and option fourth are correct this expression is equivalent to the formula for a trapezoid.
Learn more about the trapezoid here:
brainly.com/question/8643562
#SPJ1
cqn someone answer this?
Answer:
-3Step-by-step explanation:
-11/2+27/4+(-17/4)(-22+27-17)/4(-12)/4-3A rope is cut into three pleces. The lengths are given as 2ab(a - b), 3^2(a + 2b), and b^2 (2a - b).
The expression representing the total length of the rope is_____?
If a = 2 inches and b = 3 inches, the total length of the rope is ____?
inches.
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]2ab(a-b)+3a^2(a+2b)+b^2(2a-b)\\\\=2a^2b-2ab^2+3a^3+6a^2b+2ab^2-b^3\\\\=\boxed{3a^3-b^3+8a^2b}[/tex]
For a = 2, b = 3 the total is
[tex]3\cdot 2^3-3^3+8\cdot 2^2 \cdot 3\\\\=3*8-27+96\\\\=24-27+96\\\\=\boxed{93}[/tex]
Thank you
Its very confusing so sry
HELPP (ESPECIALLY PART B) Answer the questions in this part of the task based on your understanding of the definition and the standard equation for the conic you chose. part a Inspect the equation for the type of conic section you chose. What attributes are necessary to graph it? Be sure to include specific points or equations to complete your answer. part b Explain how, if you have the attributes given below for the conic you chose, you can derive its equation in standard form.
The conic section chosen is a parabola, and the attributes for graphing of
a parabola as well as the standard form of the equation are as follows;
Part A: The attribute necessary to graph the equation of the parabola are three points, including, the vertex, the y-intercept and the image of the reflection of the y-intercept across the axis of symmetry.Part B: The equation in standard form is x = -0.25·y² + y + 3Reasons:
Part A:
The equation of the conic section of a parabola is; (x - 3)² = 12·(y - 2)
The vertex form of the equation of a parabola is; y = a·(x - h)² + k
Where (h, k) = The vertex
Rearranging the given equation gives;
(x - 3)² = 12·y - 24
12·y - 24 = (x - 3)²
12·y = (x - 3)² + 24
[tex]\displaystyle y = \frac{1}{12} \cdot \left(x - 3\right)^2 + \frac{24}{12} = \frac{1}{12} \cdot \left(x - 3\right)^2 + 2[/tex]
[tex]\displaystyle y = \frac{1}{12} \cdot \left(x - 3\right)^2 + 2[/tex]
Therefore, the vertex of the parabola, (h, k) = (3, 2)
At the y-intercept, x = 0, which gives;
[tex]\displaystyle y = \frac{1}{12} \cdot \left(0 - 3\right)^2 + 2 = \frac{9}{12} + 2 = 2+\frac{3}{4}[/tex]
[tex]\displaystyle y = 2+\frac{3}{4} = 2.75[/tex]
The y-intercept = (0, 2.75)
The x-intercept is given at the point where y = 0, which gives;
(x - 3)² = 12·(0 - 2) = -24
x - 3 = √(-24) = An imaginary number
Therefore, the graph has no x-intercept
Given that a parabola is symmetrical about the vertex, we have a third
point on the parabola at the image of the y-intercept reflected across the
axis of symmetry as follows;
The y-intercept (0, 2.75) is 3 units to the left of the axis of symmetry, x = 3,
therefore, the third point will be 3 units to the right of the axis of symmetry
at the point (3 + 3, 2.75) = (6, 2.75)
Therefore, using the three points, (0, 2.75), (3, 2), and (6, 2.75), the curve
representing the parabola, (x - 3)² = 12·(y - 2), can be drawn.
Please find attached the graph of the parabola created with MS Excel
Part B; Given the attributes of the parabola; Vertex: (4, 2) and focus: (3, 2), we have;
The focus of a parabola is the point (h + p, k)
Where, (h, k) = The vertex
Therefore, by comparison, we have;
(h, k) = (4, 2)
h + p = 3
Therefore;
4 + p = 3
p = 3 - 4 = -1
The vertex form of the equation of the parabola is; (y - k)² = 4·p·(x - h)
Therefore, we get;
(y - 2)² = 4 × (-1) × (x - 4) = -4·(x - 4)
y² - 4·y + 4 = 16 - 4·x
4·x = 16 - (y² - 4·y + 4) = -y² + 4·y + 12
Which gives, the standard form as follows;
[tex]\displaystyle x = -\frac{y^2}{4} + y + 3 = -0.25 \cdot y^2 + y + 3[/tex]
Standard form of the the equation of the parabola; x = -0.25·y² + y + 3Learn more about the graph of a parabola here:
https://brainly.com/question/2489929
